Local and global tameness in Krull monoids

W. D. Gao (1) , Alfred Geroldinger (2) , Wolfgang Schmid (3)

1 CFC - Center for Combinatorics [Nankai]
2 IM - Institut für Mathematik [Graz]
3 LAGA - Laboratoire Analyse, Géométrie et Applications

Let H be a Krull monoid with finite class group G such that every class contains a prime divisor. Then the global tame degree t (H) equals zero if and only if H is factorial (equivalently, |G|=1). If |G| > 1, then D (G) <= t (H) <= 1 + D (G) ( D (G) -1 ) / 2, where D (G) is the Davenport constant of G. We analyze the case when t (H) equals the lower bound, and we show that t (H) grows asymptotically as the upper bound, when both terms are considered as functions of the rank of G. We provide more precise results if G is either cyclic or an elementary 2-group.

Mots clés: Krull monoids; non-unique factorizations; tame degree; zero-sum subsequence

Domaines: Algèbre commutative [math.AC]; Combinatoire [math.CO]

W. D. Gao, Alfred Geroldinger, Wolfgang Schmid. Local and global tameness in Krull monoids. Communications in Algebra, 2014, Special Issue Dedicated to Marco Fontana, 43 (1), pp.262-296. ⟨10.1080/00927872.2014.897585⟩. ⟨hal-00787681v2⟩